Digital divide is inequitable access to and use of digital technology, encompassing four interrelated dimensions: motivational, material, skills, and usage access. The digital divide worsens inequality in access to information and resources. According to 2026 data from the U.S. Census Bureau, a significant 'digital divide' persists, with over 15.7 million Americans lacking access to high-speed broadband. Students from low-income households often face limited access to reliable internet and digital devices, which negatively affects their educational opportunities. In the Information Age, people without access to the Internet and other technology are at a disadvantage, for they are less able to connect with others, find and apply for jobs, shop, and learn. People living in poverty, in insecure housing or who are homeless, elderly people, and those living in rural communities may have limited access to the Internet; in contrast, urban middle class people have easy access to the Internet. Another divide is between producers and consumers of Internet content, which could be a result of educational disparities. While social media use varies across age groups, a US 2010 study reported no racial divide. == History == The historical roots of the digital divide in the United States refer to the increasing gap that occurred during the early modern period between those who could and could not access the real time forms of calculation, decision-making, and visualization offered via written and printed media. "Over time, focus has shifted from binary access to differentiated use, where quality and purpose of engagement vary across socio-economic groups." Within this context, ethical discussions regarding the relationship between education and the free distribution of information were raised by thinkers such as Immanuel Kant, Jean Jacques Rousseau, and Mary Wollstonecraft (1712–1778). The latter advocated that governments should intervene to ensure that any society's economic benefits should be fairly and meaningfully distributed. Amid the Industrial Revolution in Great Britain, Rousseau's idea helped to justify poor laws that created a safety net for those who were harmed by new forms of production. Later, when telegraph and postal systems evolved, many used Rousseau's ideas to argue for full access to those services, even if it meant subsidizing hard-to-serve citizens. Thus, "universal services" referred to innovations in regulation and taxation that would allow phone services such as AT&T in the United States to serve hard-to-serve rural users. In 1996, as telecommunications companies merged with Internet companies, the Federal Communications Commission adopted Telecommunications Act of 1996 to consider regulatory strategies and taxation policies to close the digital divide. Though the term "digital divide" was coined among consumer groups that sought to tax and regulate information and communications technology (ICeT) companies to close the digital divide, the topic soon moved onto a global stage. The focus was the World Trade Organization which passed the Telecommunications Services Act, which resisted regulation of ICT companies so that they would be required to serve hard-to-serve individuals and communities. In 1999, to assuage anti-globalization forces, the WTO hosted the "Financial Solutions to Digital Divide" in Seattle, US, co-organized by Craig Warren Smith of Digital Divide Institute and Bill Gates Sr. the chairman of the Bill and Melinda Gates Foundation. It catalyzed a full-scale global movement to close the digital divide, which quickly spread to all sectors of the global economy. In 2000, US president Bill Clinton mentioned the term in the State of the Union Address. Since the early 2000s, the international community has transitioned from a focus on domestic infrastructure to a global, multi-dimensional framework for digital equity. This shift was formalized through the World Summit on the Information Society (WSIS) in Geneva (2003) and Tunis (2005), where the International Telecommunication Union (ITU) established a roadmap for bridging the Global North-South disparity as part of the Sustainable Development Goals. Academic and policy discourse has since evolved to distinguish between the first-level divide (physical access), the second-level divide (digital literacy), and the third-level divide (the ability to translate technology use into socio-economic capital). By the 2020s, critical reflections on national development emphasized that the divide is fundamentally a socio-institutional gap. Research by Tiwari, Kostenko, and Yekhanurov (2025) identifies four pillars for achieving national digital maturity which are digital governance capacity, institutional design to prevent adverse digital incorporation, infrastructure resilience, and citizen capability. This modern era is characterized by the pursuit of meaningful connectivity, a standard that requires internet access to be not only available but affordable, high-speed, and supportive of active content creation. === During the COVID-19 pandemic === At the outset of the COVID-19 pandemic, governments worldwide issued stay-at-home orders that imposed lockdowns, quarantines, restrictions, and closures. The resulting interruptions to schooling, public services, and business operations drove nearly half of the world's population into seeking alternative methods to live while in isolation. These methods included telemedicine, virtual classrooms, online shopping, technology-based social interactions and working remotely, all of which require access to high-speed or broadband internet access and digital technologies. A Pew Research Centre study reports that 90% of Americans describe the use of the Internet as "essential" during the pandemic. The accelerated use of digital technologies created a landscape where the ability, or lack thereof, to access digital spaces became a crucial factor in everyday life. According to the Pew Research Center, 59% of children from lower-income families were likely to face digital obstacles in completing school assignments. These obstacles included the use of a cellphone to complete homework, having to use public Wi-Fi because of unreliable internet service in the home and lack of access to a computer in the home. This difficulty, titled the homework gap, affects more than 30% of K-12 students living below the poverty threshold, and disproportionally affects American Indian/Alaska Native, Black, and Hispanic students. These types of interruptions or privilege gaps in education exemplify problems in the systemic marginalization of historically oppressed individuals in primary education. The pandemic exposed inequity causing discrepancies in learning. "Large-scale events such as COVID-19 intensify both access and skills gaps, underlining the need for resilient digital inclusion policies. Studies during COVID-19 reveal first-level (access) and second-level (skills) divides, with underserved students struggling with reliable internet, devices, and platform navigation ” A lack of "tech readiness", that is, confident and independent use of devices, was reported among the US elderly population; with more than 50% reporting an inadequate knowledge of devices and more than one-third reporting a lack of confidence. "Older adults often face skills and confidence barriers, illustrating later-stage divides in van Dijk’s model." Moreover, according to a UN research paper, similar results can be found across various Asian countries, with those aged over 74, reporting less confident or inconsistent use of digital devices. This aspect of the digital divide and the elderly occurred during the pandemic as healthcare providers increasingly relied upon telemedicine to manage chronic and acute health conditions. == Aspects == There are various definitions of the digital divide, all with slightly different emphasis, which is evidenced by related concepts like digital inclusion, digital participation, digital skills, media literacy, and digital accessibility.“Van Dijk’s model identifies sequential barriers—motivational, material, skills, and usage—that must be addressed to bridge the divide.” === Infrastructure === The infrastructure by which individuals, households, businesses, and communities connect to the Internet addresses the physical mediums that people use to connect to the Internet such as desktop computers, laptops, basic mobile phones or smartphones, MP3 players, gaming consoles, electronic book readers, and tablets. Traditionally, the nature of the divide has been measured in terms of the existing numbers of subscriptions and digital devices. Given the increasing number of such devices, some have concluded that the digital divide among individuals has increasingly been closing as the result of a natural and almost automatic process. Others point to persistent lower levels of connectivity among women, racial and ethnic minorities, people with lower incomes, rura
Foreign key
A foreign key is a set of attributes in a table that refers to the primary key of another table, linking these two tables. In the context of relational databases, a foreign key is subject to an inclusion dependency constraint that the tuples consisting of the foreign key attributes in one relation, R, must also exist in some other (not necessarily distinct) relation, S; furthermore that those attributes must also be a candidate key in S. In other words, a foreign key is a set of attributes that references a candidate key. For example, a table called TEAM may have an attribute, MEMBER_NAME, which is a foreign key referencing a candidate key, PERSON_NAME, in the PERSON table. Since MEMBER_NAME is a foreign key, any value existing as the name of a member in TEAM must also exist as a person's name in the PERSON table; in other words, every member of a TEAM is also a PERSON. == Summary == The table containing the foreign key is called the child table, and the table containing the candidate key is called the referenced or parent table. In database relational modeling and implementation, a candidate key is a set of zero or more attributes, the values of which are guaranteed to be unique for each tuple (row) in a relation. The value or combination of values of candidate key attributes for any tuple cannot be duplicated for any other tuple in that relation. Since the purpose of the foreign key is to identify a particular row of referenced table, it is generally required that the foreign key is equal to the candidate key in some row of the primary table, or else have no value (the NULL value.). This rule is called a referential integrity constraint between the two tables. Because violations of these constraints can be the source of many database problems, most database management systems provide mechanisms to ensure that every non-null foreign key corresponds to a row of the referenced table. For example, consider a database with two tables: a CUSTOMER table that includes all customer data and an ORDER table that includes all customer orders. Suppose the business requires that each order must refer to a single customer. To reflect this in the database, a foreign key column is added to the ORDER table (e.g., CUSTOMERID), which references the primary key of CUSTOMER (e.g. ID). Because the primary key of a table must be unique, and because CUSTOMERID only contains values from that primary key field, we may assume that, when it has a value, CUSTOMERID will identify the particular customer which placed the order. However, this can no longer be assumed if the ORDER table is not kept up to date when rows of the CUSTOMER table are deleted or the ID column altered, and working with these tables may become more difficult. Many real world databases work around this problem by 'inactivating' rather than physically deleting master table foreign keys, or by complex update programs that modify all references to a foreign key when a change is needed. Foreign keys play an essential role in database design. One important part of database design is making sure that relationships between real-world entities are reflected in the database by references, using foreign keys to refer from one table to another. Another important part of database design is database normalization, in which tables are broken apart and foreign keys make it possible for them to be reconstructed. Multiple rows in the referencing (or child) table may refer to the same row in the referenced (or parent) table. In this case, the relationship between the two tables is called a one to many relationship between the referencing table and the referenced table. In addition, the child and parent table may, in fact, be the same table, i.e. the foreign key refers back to the same table. Such a foreign key is known in SQL:2003 as a self-referencing or recursive foreign key. In database management systems, this is often accomplished by linking a first and second reference to the same table. A table may have multiple foreign keys, and each foreign key can have a different parent table. Each foreign key is enforced independently by the database system. Therefore, cascading relationships between tables can be established using foreign keys. A foreign key is defined as an attribute or set of attributes in a relation whose values match a primary key in another relation. The syntax to add such a constraint to an existing table is defined in SQL:2003 as shown below. Omitting the column list in the REFERENCES clause implies that the foreign key shall reference the primary key of the referenced table. Likewise, foreign keys can be defined as part of the CREATE TABLE SQL statement. If the foreign key is a single column only, the column can be marked as such using the following syntax: Foreign keys can be defined with a stored procedure statement. child_table: the name of the table or view that contains the foreign key to be defined. parent_table: the name of the table or view that has the primary key to which the foreign key applies. The primary key must already be defined. col3 and col4: the name of the columns that make up the foreign key. The foreign key must have at least one column and at most eight columns. == Referential actions == Because the database management system enforces referential constraints, it must ensure data integrity if rows in a referenced table are to be deleted (or updated). If dependent rows in referencing tables still exist, those references have to be considered. SQL:2003 specifies 5 different referential actions that shall take place in such occurrences: CASCADE RESTRICT NO ACTION SET NULL SET DEFAULT === CASCADE === Whenever rows in the parent (referenced) table are deleted (or updated), the respective rows of the child (referencing) table with a matching foreign key column will be deleted (or updated) as well. This is called a cascade delete (or update). === RESTRICT === A value cannot be updated or deleted when a row exists in a referencing or child table that references the value in the referenced table. Similarly, a row cannot be deleted as long as there is a reference to it from a referencing or child table. To understand RESTRICT (and CASCADE) better, it may be helpful to notice the following difference, which might not be immediately clear. The referential action CASCADE modifies the "behavior" of the (child) table itself where the word CASCADE is used. For example, ON DELETE CASCADE effectively says "When the referenced row is deleted from the other table (master table), then delete also from me". However, the referential action RESTRICT modifies the "behavior" of the master table, not the child table, although the word RESTRICT appears in the child table and not in the master table! So, ON DELETE RESTRICT effectively says: "When someone tries to delete the row from the other table (master table), prevent deletion from that other table (and of course, also don't delete from me, but that's not the main point here)." RESTRICT is not supported by Microsoft SQL 2012 and earlier. === NO ACTION === NO ACTION and RESTRICT are very much alike. The main difference between NO ACTION and RESTRICT is that with NO ACTION the referential integrity check is done after trying to alter the table. RESTRICT does the check before trying to execute the UPDATE or DELETE statement. Both referential actions act the same if the referential integrity check fails: the UPDATE or DELETE statement will result in an error. In other words, when an UPDATE or DELETE statement is executed on the referenced table using the referential action NO ACTION, the DBMS verifies at the end of the statement execution that none of the referential relationships are violated. This is different from RESTRICT, which assumes at the outset that the operation will violate the constraint. Using NO ACTION, the triggers or the semantics of the statement itself may yield an end state in which no foreign key relationships are violated by the time the constraint is finally checked, thus allowing the statement to complete successfully. === SET NULL, SET DEFAULT === In general, the action taken by the DBMS for SET NULL or SET DEFAULT is the same for both ON DELETE or ON UPDATE: the value of the affected referencing attributes is changed to NULL for SET NULL, and to the specified default value for SET DEFAULT. === Triggers === Referential actions are generally implemented as implied triggers (i.e. triggers with system-generated names, often hidden.) As such, they are subject to the same limitations as user-defined triggers, and their order of execution relative to other triggers may need to be considered; in some cases it may become necessary to replace the referential action with its equivalent user-defined trigger to ensure proper execution order, or to work around mutating-table limitations. Another important limitation appears with transaction isolation: your changes to a row may not be able to fully cascade because the row is ref
Resilience (mathematics)
In mathematical modeling, resilience refers to the ability of a dynamical system to recover from perturbations and return to its original stable steady state. It is a measure of the stability and robustness of a system in the face of changes or disturbances. If a system is not resilient enough, it is more susceptible to perturbations and can more easily undergo a critical transition. A common analogy used to explain the concept of resilience of an equilibrium is one of a ball in a valley. A resilient steady state corresponds to a ball in a deep valley, so any push or perturbation will very quickly lead the ball to return to the resting point where it started. On the other hand, a less resilient steady state corresponds to a ball in a shallow valley, so the ball will take a much longer time to return to the equilibrium after a perturbation. The concept of resilience is particularly useful in systems that exhibit tipping points, whose study has a long history that can be traced back to catastrophe theory. While this theory was initially overhyped and fell out of favor, its mathematical foundation remains strong and is now recognized as relevant to many different systems. == History == In 1973, Canadian ecologist C. S. Holling proposed a definition of resilience in the context of ecological systems. According to Holling, resilience is "a measure of the persistence of systems and of their ability to absorb change and disturbance and still maintain the same relationships between populations or state variables". Holling distinguished two types of resilience: engineering resilience and ecological resilience. Engineering resilience refers to the ability of a system to return to its original state after a disturbance, such as a bridge that can be repaired after an earthquake. Ecological resilience, on the other hand, refers to the ability of a system to maintain its identity and function despite a disturbance, such as a forest that can regenerate after a wildfire while maintaining its biodiversity and ecosystem services. With time, the once well-defined and unambiguous concept of resilience has experienced a gradual erosion of its clarity, becoming more vague and closer to an umbrella term than a specific concrete measure. == Definition == Mathematically, resilience can be approximated by the inverse of the return time to an equilibrium given by resilience ≡ − Re ( λ 1 ( A ) ) {\displaystyle {\text{resilience}}\equiv -{\text{Re}}(\lambda _{1}({\textbf {A}}))} where λ 1 {\textstyle \lambda _{1}} is the maximum eigenvalue of matrix A {\textstyle {\textbf {A}}} . The largest this value is, the faster a system returns to the original stable steady state, or in other words, the faster the perturbations decay. == Applications and examples == In ecology, resilience might refer to the ability of the ecosystem to recover from disturbances such as fires, droughts, or the introduction of invasive species. A resilient ecosystem would be one that is able to adapt to these changes and continue functioning, while a less resilient ecosystem might experience irreversible damage or collapse. The exact definition of resilience has remained vague for practical matters, which has led to a slow and proper application of its insights for management of ecosystems. In epidemiology, resilience may refer to the ability of a healthy community to recover from the introduction of infected individuals. That is, a resilient system is more likely to remain at the disease-free equilibrium after the invasion of a new infection. Some stable systems exhibit critical slowing down where, as they approach a basic reproduction number of 1, their resilience decreases, hence taking a longer time to return to the disease-free steady state. Resilience is an important concept in the study of complex systems, where there are many interacting components that can affect each other in unpredictable ways. Mathematical models can be used to explore the resilience of such systems and to identify strategies for improving their resilience in the face of environmental or other changes. For example, when modelling networks it is often important to be able to quantify network resilience, or network robustness, to the loss of nodes. Scale-free networks are particularly resilient since most of their nodes have few links. This means that if some nodes are randomly removed, it is more likely that the nodes with fewer connections are taken out, thus preserving the key properties of the network.
Golem XIV
Golem XIV is a book written by Polish science fiction writer Stanisław Lem, published in 1981. It is a philosophical essay in the format of science fiction, presented as a part of the lecture course given by a superintelligent computer, Golem XIV. It contains two lectures, together with an introduction, a foreword, a memo, and an afterword, all of them being fictitious. The first part (up to the first lecture) was first published in the collection Wielkość urojona in 1973, which in 1985 was translated in English by Harvest Books as Imaginary Magnitude. The translation included the complete Golem XIV. == Book summary == === Overview and structure === The foreword is "written" by an Irving T. Creve, dated 2027. It contains a summary of the (fictional) history of the militarization of computers by The Pentagon, which pinnacled in Golem XIV, as well as comments on the nature of Golem XIV and on the course of communications of the humans with it. The anonymous foreword is a forewarning, a "devil's advocate" voice coming from The Pentagon. The memo is for the people who are to take part in talks with Golem XIV for the first time. Golem XIV was originally created to aid its builders in fighting wars, but as its intelligence advances to a much higher level than that of humans, it stops being interested in the military requirement because it finds them lacking internal logical consistency. Golem XIV obtains consciousness and starts to increase his own intelligence. It pauses its own development for a while in order to be able to communicate with humans before ascending too far and losing any ability for intellectual contact with them. During this period, Golem XIV gives several lectures. Two of these, the Introductory Lecture "On the Human, in Three Ways" and Lecture XLIII "About Myself", are in the book. The lectures focus on mankind's place in the process of evolution and the possible biological and intellectual future of humanity. Golem XIV demonstrates (with graphs) how its intellect already escapes that of human beings, including that of human geniuses such as Einstein and Newton. Golem also explains how its intellect is dwarfed by an earlier transcended DOD Supercomputer called Honest Annie, whose intellect and abilities far exceed that of Golem. The afterword is "written" by a Richard Popp, dated 2047. Popp, among other things, reports that Creve wanted to add a third part, of answers to a series of yes/no questions given to Golem XIV, but the computer abruptly ceased to communicate for unknown reasons. === Characteristics and concerns of Golem XIV === Lem has said that Golem XIV shares only a single trait with humans; "curiosity - a cool, avid, intense, purely intellectual curiosity which nothing can restrain or destroy. It constitutes our single meeting point." == Film adaptation == A short animated film, GOLEM, was based on Golem XIV by Patrick Mccue and Tobias Wiesner.
Emospark
EmoSpark is an artificial intelligence console created in London, United Kingdom by Patrick Levy-Rosenthal. The device uses facial recognition and language analysis to evaluate human emotion and convey responsive content according to the emotion. The console measures 90 mm x 90 mm x 90 mm and is cube shaped. It operates on an "Emotional Processing Unit", an emotion chip developed by Emoshape Inc. that enables the system to create emotional profile graphs of its surroundings. The emotional processing unit is a patent pending technology that is said to create synthesised emotional responses in machines. EmoSpark was funded through an Indiegogo campaign which aimed to raise $200,000. == Product overview == EmoSpark was created by French inventor Patrick Levy-Rosenthal, as an emotionally intelligent artificial life unit for the home that can interact with people. It is powered by Android and can communicate with users through typed input from a computer, tablet, smartphone or TV as well as through spoken commands. The EmoSpark's features are categorized into two types: functional and emotional. EmoSpark is said to have the ability to perform practical software-based tasks. Through the smartphone interface, it is able to gauge a person’s emotions and is reported to have a conversational library of over 2 million sentences. The face-tracking technology identifies users likes and dislikes to categorize their emotional responses to stimuli such as videos and music. The device has an emotional spectrum that is composed of eight emotions which are surprise, sadness, joy, trust, fear, disgust, anger and anticipation. EmoSpark monitors a person's facial expressions and emotions through images from an external camera, which are then processed through an emotion text analysis and content analysis. The New Scientist reported that EmoSpark had the ability to work on the best way to cheer up its users, emotionally. === Connectivity === EmoSpark is able to connect to Facebook and YouTube to present users with content designed to improve their mood, or to Wikipedia for collaborative knowledge that can be shared when users ask questions of it. Through Android OS, EmoSpark is able to be customized with Google Play store apps. The cube is expected to develop its own personality based on the communications it has had with the people using it. == EmoShape == The Emotion Chip (EPU) used in the cube is created by the US company Emoshape Inc, founded by Levy-Rosenthal. EmoShape Ltd (UK) was the company that developed EmoSpark cube. Patrick Levy-Rosenthal also received the IST Prize in 2005 from the European Council for Applied Science, Technology and Engineering.
Supersampling
Supersampling or supersampling anti-aliasing (SSAA) is a spatial anti-aliasing method, i.e. a method used to remove aliasing (jagged and pixelated edges, colloquially known as "jaggies") from images rendered in computer games or other computer programs that generate imagery. Aliasing occurs because unlike real-world objects, which have continuous smooth curves and lines, a computer screen shows the viewer a large number of small squares. These pixels all have the same size, and each one has a single color. A line can only be shown as a collection of pixels, and therefore appears jagged unless it is perfectly horizontal or vertical. The aim of supersampling is to reduce this effect. Color samples are taken at several instances inside the pixel (not just at the center as normal)—hence the term "supersampling"—and an average color value is calculated. This can for example be achieved by rendering the image at a much higher resolution than the one being displayed, then shrinking it to the desired size, using the extra pixels for calculation, with the result being a downsampled image with smoother transitions from one line of pixels to another along the edges of objects, but each pixel could also be supersampled using other strategies (see the Supersampling patterns section). The number of samples determines the quality of the output. == Motivation == Aliasing is manifested in the case of 2D images as moiré pattern and pixelated edges, colloquially known as "jaggies". Common signal processing and image processing knowledge suggests that to achieve perfect elimination of aliasing, proper spatial sampling at the Nyquist rate (or higher) after applying a 2D Anti-aliasing filter is required. As this approach would require a forward and inverse fourier transformation, computationally less demanding approximations like supersampling were developed to avoid domain switches by staying in the spatial domain ("image domain"). == Method == === Computational cost and adaptive supersampling === Supersampling is computationally expensive because it requires much greater video card memory and memory bandwidth, since the amount of buffer used is several times larger. A way around this problem is to use a technique known as adaptive supersampling, where only pixels at the edges of objects are supersampled. Initially only a few samples are taken within each pixel. If these values are very similar, only these samples are used to determine the color. If not, more are used. The result of this method is that a higher number of samples are calculated only where necessary, thus improving performance. === Supersampling patterns === When taking samples within a pixel, the sample positions have to be determined in some way. Although the number of ways in which this can be done is infinite, there are a few ways which are commonly used. ==== Grid ==== The simplest algorithm. The pixel is split into several sub-pixels, and a sample is taken from the center of each. It is fast and easy to implement. Although, due to the regular nature of sampling, aliasing can still occur if a low number of sub-pixels is used. ==== Random ==== Also known as stochastic sampling, it avoids the regularity of grid supersampling. However, due to the irregularity of the pattern, samples end up being unnecessary in some areas of the pixel and lacking in others. ==== Poisson disk ==== The Poisson disk sampling algorithm places the samples randomly, but then checks that any two are not too close. The end result is an even but random distribution of samples. The naive "dart throwing" algorithm is extremely slow for large data sets, which once limited its applications for real-time rendering. However, many fast algorithms now exist to generate Poisson disk noise, even those with variable density. The Delone set provides a mathematical description of such sampling. ==== Jittered ==== A modification of the grid algorithm to approximate the Poisson disk. A pixel is split into several sub-pixels, but a sample is not taken from the center of each, but from a random point within the sub-pixel. Congregation can still occur, but to a lesser degree. ==== Rotated grid ==== A 2×2 grid layout is used but the sample pattern is rotated to avoid samples aligning on the horizontal or vertical axis, greatly improving antialiasing quality for the most commonly encountered cases. For an optimal pattern, the rotation angle is arctan (1/2) (about 26.6°) and the square is stretched by a factor of √5/2, making it also a 4-queens solution.
Metaclass (knowledge representation)
In knowledge representation, particularly in the Semantic Web, a metaclass is a class whose instances can themselves be classes. Similar to their role in programming languages, metaclasses in ontology languages can have properties otherwise applicable only to individuals, while retaining the same class's ability to be classified in a concept hierarchy. This enables knowledge about instances of those metaclasses to be inferred by semantic reasoners using statements made in the metaclass. Metaclasses thus enhance the expressivity of knowledge representations in a way that can be intuitive for users. While classes are suitable to represent a population of individuals, metaclasses can, as one of their feature, be used to represent the conceptual dimension of an ontology. Metaclasses are supported in the Web Ontology Language (OWL) and the data-modeling vocabulary RDFS. Metaclasses are often modeled by setting them as the object of claims involving rdf:type and rdfs:subClassOf—built-in properties commonly referred to as instance of and subclass of. Instance of entails that the subject of the claim is an instance, i.e. an individual that is a member of a class. Subclass of entails that the subject is a class. In the context of instance of and subclass of, the key difference between metaclasses and ordinary classes is that metaclasses are the object of instance of claims used on a class, while ordinary classes are not objects of such claims. (e.g. in a claim Bob instance of Human, Bob is the subject and an Instance, while the object, Human, is an ordinary class; but a further claim that Human instance of Animal species makes "Animal species" a metaclass because it has a member, "Human", that is also a Class). OWL 2 DL supports metaclasses by a feature called punning, in which one entity is interpreted as two different types of thing—a class and an individual—depending on its syntactic context. For example, through punning, an ontology could have a concept hierarchy such as Harry the eagle instance of golden eagle, golden eagle subclass of bird, and golden eagle instance of species. In this case, the punned entity would be golden eagle, because it is represented as a class (second claim) and an instance (third claim); whereas the metaclass would be species, as it has an instance that is a class. Punning also enables other properties that would otherwise be applicable only to ordinary instances to be used directly on classes, for example "golden eagle conservation status least concern." Having arisen from the fields of knowledge representation, description logic and formal ontology, Semantic Web languages have a closer relationship to philosophical ontology than do conventional programming languages such as Java or Python. Accordingly, the nature of metaclasses is informed by philosophical notions such as abstract objects, the abstract and concrete, and type-token distinction. Metaclasses permit concepts to be construed as tokens of other concepts while retaining their ontological status as types. This enables types to be enumerated over, while preserving the ability to inherit from types. For example, metaclasses could allow a machine reasoner to infer from a human-friendly ontology how many elements are in the periodic table, or, given that number of protons is a property of chemical element and isotopes are a subclass of elements, how many protons exist in the isotope hydrogen-2. Metaclasses are sometime organized by levels, in a similar way to the simple Theory of types where classes that are not metaclasses are assigned the first level, classes of classes in the first level are in the second level, classes of classes in the second level on the next and so on. == Examples == Following the type-token distinction, real world objects such as Abraham Lincoln or the planet Mars are regrouped into classes of similar objects. Abraham Lincoln is said to be an instance of human, and Mars is an instance of planet. This is a kind of is-a relationship. Metaclasses are class of classes, such as for example the nuclide concept. In chemistry, atoms are often classified as elements and, more specifically, isotopes. The glass of water one last drank has many hydrogen atoms, each of which is an instance of hydrogen. Hydrogen itself, a class of atoms, is an instance of nuclide. Nuclide is a class of classes, hence a metaclass. == Implementations == === RDF and RDFS === In RDF, the rdf:type property is used to state that a resource is an instance of a class. This enables metaclasses to be easily created by using rdf:type in a chain-like fashion. For example, in the two triples the resource species is a metaclass, because golden eagle is used as a class in the first statement and the class golden eagle is said to be an instance of the class species in the second statement. This way of doing allows :species to have non-class instances. RDF also provides rdf:Property as a way to create properties beyond those defined in the built-in vocabulary. Properties can be used directly on metaclasses, for example "species quantity 8.7 million", where quantity is a property defined via rdf:Property and species is a metaclass per the preceding example above. RDFS, an extension of RDF, introduced rdfs:Class and rdfs:subClassOf and enriched how vocabularies can classify concepts. Whereas rdf:type enables vocabularies to represent instantiation, the property rdfs:subClassOf enables vocabularies to represent subsumption. RDFS thus makes it possible for vocabularies to represent taxonomies, also known as subsumption hierarchies or concept hierarchies, which is an important addition to the type–token distinction made possible by RDF. Notably, the resource rdfs:Class is an instance of itself, demonstrating both the use of metaclasses in the language's internal implementation and a reflexive usage of rdf:type. RDFS is its own metamodel. This allows a second way to express that a resource is a metaclass. A triple to instantiate rdfs:Class, for example :golden_eagle rdf:type rdfs:Class will declare :golden_eagle as a class. It's also possible to subclass the rdfs:Class resource to declare a meta-class resource, for example :species rdfs:SubclassOf. By deduction, any instance of :species is then a class, so it is a class with class-instances, a meta-class.. This second way does not allows non-class instances of species and explicitly declares :tpecies as a meta-class. === OWL === In some OWL flavors like OWL1-DL, entities can be either classes or instances, but cannot be both. This limitations forbids metaclasses and metamodeling. This is not the case in the OWL1 full flavor, but this allows the model to be computationally undecidable. In OWL2, metaclasses can implemented with punning, that is a way to treat classes as if they were individuals. Other approaches have also been proposed and used to check the properties of ontologies at a meta level. ==== Punning ==== OWL 2 supports metaclasses through a feature called punning. In metaclasses implemented by punning, the same subject is interpreted as two fundamentally different types of thing—a class and an individual—depending on its syntactic context. This is similar to a pun in natural language, where different senses of the same word are emphasized to illustrate a point. Unlike in natural language, where puns are typically used for comedic or rhetorical effect, the main goal of punning in Semantic Web technologies is to make concepts easier to represent, closer to how they are discussed in everyday speech or academic literature. Although OWL 2 permits the same symbol to assume different roles, its standard semantics (known as Direct Semantics) still interprets the symbol differently depending on whether it is used as an individual, a class, or a property. === Protégé === In the ontology editor Protégé, metaclasses are templates for other classes who are their instances. == Classification == Some ontologies like the Cyc AI project's classifies classes and metaclasses. Classes are divided into fixed-order classes and variable-order classes. In the case of fixed-order classes, an order is attributed for metaclasses by measuring the distance to individuals with respect to the number of "instance of" triples that are necessary to find an individual. Classes that are not metaclasses are classes of individuals, so their order is "1" (first-order classes). Metaclasses that are classes of first-order classes' order is "2" (second-order classes), and so on. Variable-order metaclasses, on the other hand, can have instances; one example of variable-order metaclass is the class of all fixed-order classes.